Mensuration 2D

Definition of Mensuration Maths :

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.

What is Mensuration ?

Mensuration is a subject of geometry. Mensuration deals with the size, region and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.

Introduction to Menstruation: Important Terms

Until we switch to the list of important formulas for measurement, we need to clarify certain important terms that make these formulas for measurement:

Area (A):

The area is called the surface occupied by a defined closed region. It is defined by the letter A and expressed in a square unit.

Perimeter (P): 

The total length of the boundary of a figure is called its perimeter. Perimeter is determined of only two-dimensional shapes or figures. It is the continuous line along the edge of the closed vessel. It is represented by P and measures are taken in a square unit.

Volume(V):

Volume is the amount of space inside a 3- dimensional figure. It is measured  in cubic units.  A cubic cm is a cube that is 1 cm wide, 1 cm long, and 1 cm high
Another  way to think volume is to find the number of cubes necessary for building the figure

  Volume=(Area of base) x (height)

What is a 2D Shape ?

A 2D diagram is a shape laid down on a plane by three or more straight lines or a closed segment. Such forms do not have width or height; they have two dimensions-length and breadth and are therefore called 2D shapes or figures. Of 2D forms, area (A) and perimeter (P) is to be determined.

2 Diamensional shape:

• Quadrilateral ( Square, Rectangle,Parallogram,Trapezium, Rhombus)
• Triangle
• Circle/ Semicircle

Square:

Properties of a square

• All sides and angles are congruent.
• Opposite sides are parallel to each other.
• The diagonals are congruent.
• The diagonals are perpendicular to and bisect each other.
• A square is a special type of parallelogram whose all angles and sides are equal.
• Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

Important formulas for Squares

• If ‘L’ is the length of the side of a square then length of the diagonal = a √2.
• Area = a².
• Perimeter = 4a

Rectangle

A rectangle is a two-dimensional plane figure with four sides. A rectangle is a four-sided polygon in which the opposite sides are parallel and equal to each other. It is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. The rectangle is a special type of parallelogram with all its angles equal. A rectangle with four equal sides is known as a square. Now let us learn the properties of rectangle in this article.

Rectangle Properties

The fundamental properties of rectangles are:

• A rectangle is a quadrilateral
• The opposite sides are parallel and equal to each other
• Each interior angle is equal to 90 degrees
• The sum of all the interior angles is equal to 360 degrees
• The diagonals bisect each other
• Both the diagonals have the same length
• A rectangle with side lengths a and b has the perimeter as 2a+2b units
• A rectangle with side lengths a and b has the area as: ab sin 90 = ab square units
• The sum of the interior angles is equal to 360 degrees
• A diagonal of a rectangle is a diameter of its circumcircle
• If a and b are the sides of a rectangle, then the length of each diagonal is: d=√a²+b²
• The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle
• If the two diagonals bisect each other at right angles, then the rectangle is known as a square
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangle .
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangle

Important formulas for Rectangle

• If ‘L’ is the length of the rectangle  and ‘B’ is the breadth of the rectangle then 
• Area = L x B
• Perimeter =